Search results
Results from the WOW.Com Content Network
With the new operations, the implementation of AVL trees can be more efficient and highly-parallelizable. [13] The function Join on two AVL trees t 1 and t 2 and a key k will return a tree containing all elements in t 1, t 2 as well as k. It requires k to be greater than all keys in t 1 and smaller than all keys in t 2.
The weak AVL tree is defined by the weak AVL rule: Weak AVL rule: all rank differences are 1 or 2, and all leaf nodes have rank 0. Note that weak AVL tree generalizes the AVL tree by allowing for 2,2 type node. A simple proof shows that a weak AVL tree can be colored in a way that represents a red-black tree.
Under this framework, the join operation captures all balancing criteria of different balancing schemes, and all other functions join have generic implementation across different balancing schemes. The join-based algorithms can be applied to at least four balancing schemes: AVL trees, red–black trees, weight-balanced trees and treaps.
The code above uses OCaml's default hash function Hashtbl.hash, which is defined automatically for all types. To use a modified hash function, use the functor interface Hashtbl.Make to create a module, such as with Map. Finally, functional maps (represented as immutable balanced binary trees): #
Scapegoat trees are unusual in that deletion is easier than insertion. To enable deletion, scapegoat trees need to store an additional value with the tree data structure. This property, which we will call MaxNodeCount simply represents the highest achieved NodeCount.
For infinite trees, simple algorithms often fail this. For example, given a binary tree of infinite depth, a depth-first search will go down one side (by convention the left side) of the tree, never visiting the rest, and indeed an in-order or post-order traversal will never visit any nodes, as it has not reached a leaf (and in fact never will ...
Deletion from vEB trees is the trickiest of the operations. The call Delete(T, x) that deletes a value x from a vEB tree T operates as follows: If T.min = T.max = x then x is the only element stored in the tree and we set T.min = M and T.max = −1 to indicate that the tree is empty.
Both insertion and deletion require () time, with being the total number of intervals in the tree prior to the insertion or deletion operation. An augmented tree can be built from a simple ordered tree, for example a binary search tree or self-balancing binary search tree, ordered by the 'low' values of the intervals. An extra annotation is ...